Make the Pesto: Add 2 packed cups of arugula to a food processor or blender, along with the almonds, grated cheese, preserved lemon, garlic, and salt. Blend everything until finely chopped. While the machine is running, slowly pour in the olive oil and process until the mixture is smooth and creamy.
Warm the Beans: Heat the white beans in the microwave for about 1 minute, or warm them in a small pot over the stove for 2 to 3 minutes. The beans should be slightly warm, but avoid overheating them.
Combine the Pesto and Beans: In a mixing bowl, toss the warm beans with the arugula pesto. Adjust the seasoning to your taste, adding more salt, lemon juice, or black pepper if needed.
Assemble the Salad: In a large bowl, toss the remaining fresh arugula with a drizzle of olive oil, a splash of lemon juice, salt, and black pepper. Arrange the dressed arugula on a serving platter, then spoon the pesto-coated beans on top. Sprinkle the salad with shaved shallots or red onion, if using, and serve immediately.